Ceteris paribus is a Latin phrase used to describe the circumstances when we assume aspects other than the one being studied to remain constant.
In particular, we examine the influence of each explanatory variable, assuming that effects of all other variables are unchanged. Ceteris-paribus (CP) profiles are one-dimensional profiles that examine the curvature across each variable. In essence it shows a conditional expectation of the dependent variable for the particular independent variable Ceteris-Paribus profiles are also a useful tool for sensitivity analysis.
We can make local diagnostics with CP profiles using Fidelity plot. The idea behind fidelity plots is to select several observations that are closest to the instance of interest. Then, for the selected observations, we plot CP profiles and check how stable they are. Additionally, using actual value of dependent variable for the selected neighbours, we can add residuals to the plot to evaluate the local fit of the model.
- Identification of neighbors: One can use the similarity measures like Gower similarity measure to identify the neighbors.
- Calculation and visualization of CP profiles for the selected neighbors: Once nearest neighbors have been identified, we can graphically compare CP profiles for selected (or all) variables. We can say that model predictions are not stable around the instance of interest, if profiles are quite apart from each other and the predictions are stable if we don’t see a large variation for the small changes in the explanatory variables i.e. in nearest neighbors.
- Analysis of residuals for the neighbors: We can plot the histograms of residuals for the entire dataset. It can give us idea about average performance of the model.
Local-fidelity plots may be very helpful to check if the model is locally additive and locally stable but for a model with a large number of explanatory variables we may end up with a large number of plots. The drawback is these plots are quite complex and lack objective measures of the quality of the model fit. Thus, they are mainly suitable for an exploratory analysis.